Sealing Teeth Effects on Natural Frequencies of a Short Cylindrical Shell

Abstract:

Natural frequencies are calculated for a short cylindrical shell based on semi-analytical method of transfer matrix, especially considering the structural effects of sealing teeth. The thin wall shell with some sealing teeth can be divided into finite segments where the diameters are different. According to the theory of the state vector expression of a structure cross-section, a first-order ordinary differential equation referring to state vectors of continuous segment sections of a short cylindrical shell is established based on governing equations of thin cylindrical shell. Then a total transfer matrix of the shell with sealing teeth is obtained after producing all the transfer matrices of all the segments. The boundary conditions investigated in the study are free-free, free-clamped and clamped-clamped of the two ends of the shell. The natural frequencies can be solved by precise integration of the differential equation of the whole shell with divided segments. The obtained numerical examples show that the sealing teeth have influence on the frequency values of higher circumferential modes, and they also have influence on the natural frequencies in different boundary conditions. The results by the proposed method are also compared with those of finite element method.

• Periodical: Advanced Engineering Forum (Volumes 2-3)
• Pages: 1021-1026
• DOI: https://doi.org/10.4028/www.scientific.net/AEF.2-3.1021
• Online since: December 2011
• Authors: Yu Wang, Hai Yang Duan, Gao Ming Qin, Zhong Luo, Qing Kai Han
• Keywords: Natural Frequency, Sealing Teeth, Short Cylindrical Shell, Transfer Matrix Method (TMM)

References

[1] Fanglin Zong, Yansheng Liu, Qiping Hu, State space method for axis-symmetrical bending problems of cylindrical shells with variable thicknesses, J Tsinghua Univ (Sci & Tech), 11(2008) 1845-1848 (in Chinese).

[2] Xuebin Li, Energy method for free vibration analysis of ring-stiffened cylindrical shells, Journal of Ship Mechanics, 2(2001) 73-81(in Chinese).

[3] Yu Xiang, The exact form of transfer matrix for analysis of free vibration of structures, Journal of Vibration and Shock, 2(1999): 69–74. (in Chinese).

[4] Baoli Sun, Yuping Ni, Spline finite-point method used in dynamic analysis of cylindrical shell with variable thickness, J. of Wuhan Univ Hydr. & Elec Eng., 1(1992) 5-11(in Chinese).

[5] Little R. W., P, Elasticity, New Jersey: Prentice-Hall Inc, (1973).

[6] Timoshenko, S., Theory of Plates and Shells, McGraw-Hill Book Company, Inc, (1959).

[7] Haidong Su, Yuying Huang, A transfer matrix method for analyzing revolutionary shells, Engineering Mechanics, 9(2008, ) 1-6, 12(in Chinese).

[8] Suying Zhang, Zichen Deng, An improved precise integration method for nonlinear dynamic system, Mechanics Research Communications, 1(2003) 33-38(in Chinese).

DOI: 10.1016/s0093-6413(02)00311-7